Hilbert's Twenty-Fourth Problem

Summary: This paper discusses the problem that almost made it among Hilbert's twenty-three unsolved problems presented in his epochal ICM address. The problem, on defining a notion of simplicity for mathematical proofs, is relevant to foundations and philosophy of mathematics.

Rüdiger Thiele is a historian of mathematics who studied both mathematics and physics, receiving his Ph.D. in mathematics from Martin Luther University of Halle-Wittenberg (Germany) and his habilitation in the history of physical sciences from University of Hamburg. In 1996 he was awarded the Forder Prize of the German Academy of Natural Sciences, Leopoldina. Since 1986 he has held a position as Privatdozent in Mathematics at the University of Leipzig. He has been a visiting professor and research scholar at the Universities of Bonn, Mainz, Munster, and Toronto and is vice president of the Euler Society in the USA. While having diverse research interests in the history of mathematics, his main field of research is the history of the calculus of variations. His publications include a biography of Leonhard Euler and a booklet on mathematical proofs. Recently he edited the Festschrift "Mathesis" in honor of M. Schramm. His other interests include philosophy and, above all, music.